Question: $K$ is the midpoint of $\overline{JL}$ $J$ $K$ $L$ If: $ JK = 7x + 3$ and $ KL = 8x + 1$ Find $JL$.
A midpoint divides a segment into two segments with equal lengths. ${JK} = {KL}$ Substitute in the expressions that were given for each length: $ {7x + 3} = {8x + 1}$ Solve for $x$ $ -x = -2$ $ x = 2$ Substitute $2$ for $x$ in the expressions that were given for $JK$ and $KL$ $ JK = 7({2}) + 3$ $ KL = 8({2}) + 1$ $ JK = 14 + 3$ $ KL = 16 + 1$ $ JK = 17$ $ KL = 17$ To find the length $JL$ , add the lengths ${JK}$ and ${KL}$ $ JL = {JK} + {KL}$ $ JL = {17} + {17}$ $ JL = 34$